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HYPERSPECTRAL IMAGE

CLASSIFICATION BASED ON

SPECTRAL

AND

GEOMETRICAL FEATURES

Bin Luo and Jocelyn Chanussot

GIPSA-Lab, 961 rue de la Houille Blanche, 38402 Grenoble, France.

([email protected])

G

[email protected])

ABSTRACT

In this paper, we propose to integrate geometrical features,

such as the characteristic scales

of

structures, with spectral

features for the classification of hyperspectral images. The

spectral features which only describe the material

of

struc

tures can not distinguish objects made by the same material

but with different semantic meanings (such as the roofs

of

some buildings and the roads). The use of geometrical fea

tures is therefore necessary. Moreover, since the dimension

of

a hyperspectral image is usually very high, we use linear un

mixing algorithm to extract the endmemebers and their abun

dance maps in order to represent compactly the spectral infor

mation. Afterwards, with the help of these abundance maps,

we propose a method based on topographic map

of

images to

estimate local scales of structures in hyperspectral images.

The experiment shows that the geometrical features can

improve the classification results, especially for the classes

made by the same material but with different semantic mean

ings. When compared to the traditional contextual features

(such as morphological profiles), the local scale feature pro

vides satisfactory results without considerably increasing the

feature dimension.

1. INTRODUCTION

The classification

of

hyperspectral remote sensing images is

a challenging task, since the data dimension is considerable

for traditional classification algorithms, typically several hun

dreds of spectral bands are acquired for each image. These

spectral bands can provide very rich spectral information

of

each pixel in order to identify the material of the objects.

However, the spectral information alone sometimes does not

allow the separation of structures. For example, the roofs of

some buidings and the roads can be made by the same ma

terial (alsphalt). Therefore, contextual information, geomet

rical features for example, is necessary for classification task

of

hyperspectral images.

The major difficulty to calculate the contextual informa

tion

of

hyper spectral images is the high dimension

of

the data.

This work is funded by French ANR project VAHINE.

978-1-4244-4948-4/09/ 25.00 © 2009 IEEE

Toreduce the data dimension, both supervised and non super

vised methods are proposed. The supervisedmethods, such as

band selection [1] [2], Decision Boundary feature extraction

and Non-Weighted feature extraction [3], transform the data

according to the training set in order to improve the separabil

ity

of

the data. However, the supervised methods depend on

the quality

of

training set. The unsupervised methods, such

as PCA (principle component analysis) or ICA (independant

component analysis), optimise some statistical criteria (such

as the most un correlated components or the most independant

components) to project the data onto a sub space with lower

dimension. The application

of

these methods on hyperspec

tral data can be found in [4] [5] [6]. However, the components

obtained by optimising the statistical criteria do not neces

sarily have physical meanings. In this paper, we propose to

use VertexComponent Analysis (VCA) to reduce the dimen

sion of hyperspectral data [7]. We suppose that the spectrum

of

each pixel is a linear mixture

of

the spectra

of

different

chemical species (refered as endmembers). This linear mix

ture model is physically valid for the reflectance

of

the surface

of the Earth without being affected by the aerosol. The VCA

can separate the spectra

of

these endmembers and estimate

their spatial abundances. Since the number

of

the endmem

bers is much less than the number

of

spectral bands, these

abundance maps can be considered as a compact represen

tation

of

spectral information provided by the hyperspectral

image.

In order to extract the contextual information from remote

sensing images, one can find the methods based on Markov

Random Field (MRF) [8]. However, the MRF based meth

ods provide only statistical information on the neighborhood

of the considered pixel. Another family of methods for con

textual information extraction are based on morpholigical op

erators, which allow to extract descriptive features, such as

the geometrical features about the structures [9]. [4] [5] ex

tract the extended morphological profiles (EMP) of the princi

ple components

of

hyperspectral images for the classification.

However, since all morphological methods require a structred

element, the features extracted by such methods depend on

the used structured element. Moreover, EMP increase con-


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Fig.

1.

Scheme of the paper.

siderably the feature dimension. For example, in order to de

scribe the geometrical information of one pixel on a principle

component, the EMP method in [4] [5] uses 8 values. In [10],

based on topographic map of gray scale image, the authors

define a characteristic scale of each pixel in panchromatic re

mote sensing images. The main idea isthat for each pixel, the

contrasted structure containing it is extracted, and the scale

of this structure is defined as the scale of this pixel . In this

paper, we try to extend the algorithm presented in [10] for

extracting a local characteristic scale for each pixel on hyper

spectral imageswith the help

of

the abundancemaps obtained

by VCA. The main advantages

of our proposed method when

compared to EMP are two-fold. At one hand, no structured

element is required for this method. Secondly, we use only

one value (the local scale) to describe the geometrical feature

of

a spatial position rather than the EMP which need many

values.

I= MS

n

2. LINEAR UNMIXING OF HYPERSPECTRAL DATA

We note X the matrix representing the hyperspectral im

age cube , where X = {X I

,X 2

, ,X N

a

}

and Xk =

{ XI

,k

, X2 ,k , . . .

x

,,, d

T

Xl

,k

is the value of the kth pixel at

the lth band. We assume that the spectrum

of

each pixel is a

linear mixture of the spectra of

N;

endmembers, leading to

the following model:

where M

=

{m-, m2,

.. .

,

m

NJ

is the mixing matrix, where

m., denotes the spectral signature of the nth endmember.

S = { 5 I , 5 2 ,

. .

. , 5N o } T is the abundance matrix where

5

n

=

{Sn

, l , S n ,2 , . . . , S n , N

a

} S n

,k

E

[0 ,1] is the abun

dance

of

the nth endmember at the kth pixel). n stands for

the additive noise of the image. In [7] , the Vertex Compo

nent Analysis (VCA) is proposed as an effecient method for

extracting the endmembers which are linearly mixed. The

main idea is to extract the vertex of the simplex formed by

M which contains all the data vectors in X. The sum of the

abundances of different endmembers at each pixel is one, i.e,

L : Sn

,k

= 1, which is called the sum-fa-one condition.

Therefore the data vectors Xl are always inside a simplex of

which the vertex are the spectra

of

the endmembers. VCA it

eratively projects the data onto the direction orthogonal to the

subspace spanned by the already determined endmembers.

And the extreme of this project ion is the new endmember

signature. The algorithm stops when all the

p

endmembers

are extracted, where p is the number of endmembers. Even

though the number of endmembers is much smaller than the

number of spectral bands, i.e,

p


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map [11], which can be obtained by Fast Level Set Trans

formation (FLST) [12], represents an image by an inclusion

tree

of

the shapes (which are defined as the connected com

ponents of level sets) . An example of such inclusion tree is

shown in Figure 2 . For each pixel

x,

y), there is a branch

of

shapes fi(X,y)

f

i

l

C

f i) containing it. Note

l J

i) the

gray level of the shape fi(X,y), S(Ji) its area and

P J

i)

its perimeter. The contrast

of

the shape fi(X,y) is defined

as C Ji) = II Ji+ l ) - I( Ji) The most contrasted shape

Ji(x,y)

of

a given pixel is defined as the shape containing

this pixel,

of

which the contrast is the most important, i.e.

•

(a)

A :5255

E(x,y)

= S J

i(x,y))jP(Ji(x,y)).

3

(5)

D :5128

G

C ,,40

F 2:150

(b)

H :50

E(x,y)

=

Eft(x, y)

E 2;128

Fig. 2. Example

ofFLST:

(a) Synthetic

image;

(b) Inclusion

tree obtained with FLST.

object is mainlymade by the

nth

endmember, the scale values

calculated on the abundance maps of the other endmembers

for this object have no meaning. Therefore, we try to define

one single scale value for each pixel which corresponds to

the scale of this pixel on the most significant abundancemap.

More precisely, since the values of different abundance maps

are comparable, the characteristic scale at the spatial position

x,

y for a hyperspectral image is defined as

8 x ,y =

{ll

x ,y ,

.. .

INc(x ,y ,E(x ,y } .

6

where n

=

argmaxn{C(Jin(x,y))}.

The feature vector

8 x,

y) ofa given pixel (x, y) used for

classification contains the values of the simplified image of

all the abundance maps and its local scale defined by Equa

tion (5), i.e.

In this section, we use the features defined by Equation (6)

to classify a hyperspectral image taken by the instrument RO

SIS (Reflective Optics System Imaging Spectrometer) over

the University

of

Pavia, Italy (see Figure 3(a)). The im

age (with a spatial resolution of 1.3m contains 340 x 610

pixels and 103 spectral bands covering visible and near in

frared light. The image is manually classified into 9 classes

4.

EXPERIMENT

(4)

x y _ L (k ,l )E ; (X,y )

k,

l

S(Ji(x, y))

The scale of this pixel E(x,y) is defined as the area of the

most contrasted shape divided by its perimeter, i.e.

Since the optical instruments always blur remote sensing im

ages, several shapes with very low contrasts can belong to

the same structure. In order to deal with the blur, the au

thors

of

[10] propose a geometrical criterion to cumulate the

contrasts of the shapes corresponding to one given structure.

The idea is that the difference

of

the areas

of

two succesive

shapes (for example f i and fi+l) corresponding to a same

structure is proportional to the perimeterof the smaller shape,

i.e.

S J

i+l) -

S J

i)

> P J

i), where> is a constant. It is

shown in [10] that this local scale corresponds very well to

the size of a structure and it is a very significant feature for

characterizing a structure in remote sensing images. Remark

that the most contrasted shapes extracted in an image form a

partition

of

this image. We can therefore have a simplified

image by defining the value of each pixel as the mean value

of

the gray levels

of

the pixels in its most contrasted shape,

i.e. the value of

x, y

in the simplified image is

where I( k, l) is the gray level

of

the pixel (k,l) in the orig

inal image. This value is more significant for characterizing

spectrally the pixel than its original gray level since it takes

into account the context pixels.

In order to extend the estimation of local scale to hyper

spectral images, the scales on all the abundance maps

of

the

p endmembers obtained by veA are first computed. There

fore, for each spatial position

x,

y in an hyperspectral im

age, there are p scale values. For the pixel

(x, y

on the

nth

abundancemap, we note

En(x, y)

its local scale calculated by

Equation (3), Ji

n

(x ,

y

the most contrasted shape extracted

,

by Equation (2), and In(x,y) its value

of

the simplified im

age defined by Equation (4). The simplest way to use the scale

features

ofa

pixel is to use all the En(x, y) values as features

for classification. However, the major drawback is that if an

Ji(x,y) = argmax{C Jj x , y)} (2)

J


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5.

CONCLUSION

(c)b)a)

Poin ts in Tra ining S

t

I

Thematic Colour

I

Trees 524

Asphalt

I I

Bitumen

375

Gravel

392

I I

(painted) metal sheets

265

Shadow

I

I

Self-Blocking Bricks

Meado

ws

I 1

Bare So il 53 2

Fig. 4. Definitions

of

the classes.

In this article, we have proposed to integrate geometrical fea

ture, the characteristic scales of structures, for the classifica

tion

of

hyperspectral images. In order to reduce the dimension

of

the data, we used a linear unmixing algorithm to extract the

the class

of

Meadows, which is not well defined inthe ground

truth.

It has to be remarked that by using only the spectral in

formation (i.e. the spectrum

of

each pixel), it is very difficult

to distinguish the class Asphalt and Bitumen, since they are

made by the same material. According to the ground truth

of

Figure 3(c), the only difference is that Asphalt is used for

the roads while Bitumen is used for the building roofs. How

ever, it can be seen from Figure 6(a) that the scale values

of

the pixels on the building roofs are very different from the

scales

of

the pixels on the roads. Therefore the classification

results

of

these two classes by using the feature vectors 8 are

much more accurate. This phenomenon can be illustrated by

Figure 6(d)-(t), where we have zoomed the classification re

sults obtained by using original data and the feature vectors

8 on a building roof made by bitumen.

can be seen that

the building roof and the road are classified as the same class

in Figure 6(e). In contrary, by adding the local scale feature,

these two structures are well separated.

Fig. 3. (a) Image

of

Pavia University (R-band 90, G-band 60,

B-band 40); (b) Training set; (d) Test set.

and the definitions of these classes are shown in Figure 4.

For classification purpose, the training set contains

3921

pix

els (see Figure 3(b)) while the test set contains 42776 pix

els (see Figure 3(c)). Since in this image, there are mainly

3 endmembers present (vegetation, bare soil and metal root),

we extract 3 endmembers and their abundance maps by us

ing VCA (see Section 2), which are shown in Figures 5(a)

(c). Afterwards we compute the simplified images

of

these

abundance maps by using Equation (4). The simplified im

ages are shown in Figure 5(d)-(t). According to Equation (5),

we estimate the local scale for each pixel of this image. The

scale map is shown in Figure 6(a). Therefore the feature vec

tor

8 x ,y

ofa pixel

(x ,y

defined by Equation (6) contains

only 4 values: 3 values

of

the simplified abundance maps

l l X,y),12(x,y), la(x,y)) and one scale value (E(x,y)).

We have classified the image by using the original hy

perspectral data (all

103

bands) and the feature vector 8 de

fined by Equation (6). Kernel methods are proved to be ef

fecient algorithms for hyperspectral image classification. [13]

Therefore, we use the Support Vector Machine (SVM) with

Gaussian kernel as classifier. The optimal scale parameter

of

Gaussian kernel is selected by 5-fold cross validation on the

training set.

The overall accuracies and the classification accuracies of

each class for both cases are shown in Table 1. In Figure 6(b)

and (c), the classification results obtained on the whole im

age is shown. In [5], the authors proposed to use PCA and

Kernel PCA (KPCA) to reduce the dimension

of

hyperspec

tral images. Extended Morphological Profiles (EMP) are then

extracted from the principle components obtained by PCA (3

principle components are extracted) or KPCA

(12

principle

components are extracted) as features for classifying the hy

perspectral image. In Table 1, we show the classification re

sults obtained in [5] on the same data set by using SVM with

Gaussian kernel.

It can be seen that by using the features proposed in our

article, the classification results improve considerably when

compared to the results obtained on original hyperspectral

data. Recall that the length

of

the feature vector 8 for each

pixel is only 4 which ismuch less than the number

of

spectral

bands

(103).

Moreover, the results obtained by using PCA

and EMP are very similar with the results obtained by the

features proposed, since we have previously mentioned that

the major information described by EMP on a pixel is its lo

cal scale. Indeed, the local scale

of

a pixel can be considered

as the width

of

the morphological filter by which the absolute

differential EMP value reaches its maximum. However, the

number of features extracted by PCA and EMP is 27, which

is much larger than the number

of

features in 8. The results

obtained by using KPCA and EMP are better than the results

obtained by using 8 and the results by using PCA and EMP.

However, the feature dimension, which is

108,

is even higher

than the dimension of original data

(103).

And the improve

ment of classification accuracies is mainly concentrated on


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Feature Original data Feature vector e

EMPp

C [ j

EMPK A[5j

Number

of

features 103

4

27 108

Overall accuracy 76 .01 91.54 92 .04 96 .55

Tree

98.59

94.52 99.22

99.35

Asphalt 78.16 96 .27 94 .60 96 .23

Bitumen 89 .02 99 .32 98.87 99 .10

Gravel 64 .55 84 .61 73.13 83 .66

(painted) metal sheets

99.47 99.55 99.55 99.48

Shadow

99.89 96.30 90.07

98.31

Self-Blocking Bricks 91.01

99.70 99.10 99.46

Meadows 64.23 85.80 88.79 97.58

Bare Soil 82 .72 96.56 95 .23 92 .88

Table 1. Classification results

(f)

e)

(b)

(d)

(a)

ig 6. (a) Scale map of the hyperspectral image, bright pixel

correspondsto big scale while dark pixel correspondsto small

scale; (b) Supervised classification results obtained on orig

inal data set; (c) Supervised classification results obtained

on the feature set obtained by Equation (6). (d)- (f ):

Zoom

around a bui lding on the: (d) original image; (e) classi fica

tion results of (b); (f) classification results of (c).

(f)

(c)

(e)

(b)

a)

(d)

ig 5. (a)-(c) Abundance maps of the 3 endmembers ex

tracted by VCA ; (d)-(f) the simplified images

of

these abun

dance maps.


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endmembers and their abundance maps contained in a hyper

spectral image. The abundance maps can be considered as a

compact representation of spectral information of this image,

since the number

of

endmembers contained in a hyperspec

tral image is much smaller than the numberof spectral bands.

With the help

of

these abundance maps, we extend the method

proposed in [10] to hyperspectral images to estimate the char

acteristic scales

of

the structures. The experiments show that

the use of the scale feature, the classification results improve

considerably, especially for the objects made by the same ma

terial but with different semantic meanings. By using the fea

tures proposed, the classification results are very similar to

the results obtained by using the methods based on PCA and

EMP, even though the number

of

features proposed is much

less.

Acknowledgement The authors would like to thank Pro

Paolo Gamba, University

of

Pavia, for providing the data and

the ground truth of the classification.

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